Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Thursday, May 29, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Gábor Fejes Tóth (Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Budapest, Hungary)

Shortest path among circles

Given a packing of open unit circles, any two points lying outside the circles at distance $d$ from one another can be connected by a path evading the circles and having length at most ${2\pi\over\sqrt{27}}(d-2)+\pi$. This bound cannot be improved for values of the form $2(k\sqrt3+1)$. Can a packing of incongruent circles with radii at most 1 force us to a greater detour? The answer is yes, but concerning this problem we have to be satisfied with weaker upper and lower bounds for the length of the shortest path.

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